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<title>Problem 2489. -- Random Sequence -- 衡阳八中OJ离线版-2012-02-29</title><center><h2>2489: Random Sequence</h2><span class=green>Time Limit: </span>1 Sec&nbsp;&nbsp;<span class=green>Memory Limit: </span>128 MB<br><span class=green>Submit: </span>86&nbsp;&nbsp;<span class=green>Solved: </span>20<br>[<a href='submitpage.php?id=2489'>Submit</a>][<a href='problemstatus.php?id=2489'>Status</a>][<a href='bbs.php?id=2489'>Discuss</a>]</center><h2>Description</h2><div class=content><div class="panel_content"><span style="font-size: medium">There is a random sequence L whose element are all random numbers either -1 or 1 with the same possibility. Now we define MAVS, the abbreviate of Maximum Absolute Value Subsequence, to be any (if more than one) subsequences of L whose absolute value is maximum among all subsequences. Given the length of L, your task is to find the expectation of the absolute value of MAVS.</span></div>
<p></p></div><h2>Input</h2><div class=content><p><span style="font-size: medium">There is only one input file. The first line is the number of test cases T. T positive integers follow, each of which contains one positive number not greater than 1500 denoted the length of L.<br />
</span></p>
<div class="panel_bottom"><span style="font-size: medium">&nbsp;</span></div>
<p><span style="font-size: medium">给你一个数字L,代表数字串长。这个数字串每个元素为1或-1.</span></p>
<p><span style="font-size: medium">那么就有这个数列有2^L种可能。</span></p>
<p><span style="font-size: medium">现对每个可能的数字串，求其连续子串和，并将和取绝对值，记下最大的那个值。</span></p>
<p><span style="font-size: medium">再求出所有这些值的总和。</span></p>
<p><span style="font-size: medium">输入总和/2^L</span></p></div><h2>Output</h2><div class=content><p><span style="font-size: medium">For each test case, output the expectation you are required to calculate. Answers are rounded to 6 numbers after the decimal point.(as shown in the sample output)<br />
</span></p></div><h2>Sample Input</h2>
			<div class=content><span class=sampledata>3<br />
1<br />
5<br />
10<br />
</span></div><h2>Sample Output</h2>
			<div class=content><span class=sampledata>Case 1: 1.000000<br />
Case 2: 2.750000<br />
Case 3: 4.167969<br />
</span></div><h2>HINT</h2>
			<div class=content><p><p>当输入2时，有</p><br />
<p>1 1</p><br />
<p>1 -1</p><br />
<p>-1 1</p><br />
<p>-1 -1</p><br />
<p>这四种可能，其对应的值分别为(2+1+1+2)=6</p><br />
<p>6/4=1.5</p></p></div><h2>Source</h2>
			<div class=content><p><a href='problemset.html?search=acm 2011 福州'>acm 2011 福州</a></p></div><center>[<a href='submitpage.php?id=2489'>Submit</a>][<a href='problemstatus.php?id=2489'>Status</a>][<a href='bbs.php?id=2489'>Discuss</a>]</center>﻿<br>

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